Question

The Sisyphean Company has a bond outstanding with a face value of​ $1000 that reaches maturity in 15 years. The bond certificate indicates that the stated coupon rate for this bond is​ 8% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is​ 7.5%, then the price that this bond trades for will be closest​ to:

Answer 1

The price that bond is trading for is closest to $1,044.57

Step-by-step explanation:

The price of the bond can be computed using the present value formula in excel which is given as =pv(rate,nper,pmt,fv)

rate is the yield to maturity of 7.5% divided by 2 since the bond is a semi-annual interest paying bond

nper is the year to maturity multiplied by 2 i.e 15*2=30

pmt is the semi-annual interest payable by the bond i.e 8%/2*$1000=$40

fv is the future value of the bond at redemption which is $1000

=pv(3.75%,30,40,1000)

pv= $1,044.57

Answer 2

The Price of this bond is $1,044.57

Step-by-step explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. Both of these cash flows discounted and added to calculate the value of the bond.

According to given data

Face value of the bond is $1,000

Coupon payment = C = $1,000 x 8% = $80 annually = $40 semiannually

Number of periods = n = 15 years x 2 = 30 period

Market Rate = 7.5% annually = 3.75% semiannually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond = 40 x [ ( 1 - ( 1 + 3.75% )^-30 ) / 3.75% ] + [ $1,000 / ( 1 + 3.75% )^30 ]

Price of the Bond = $713.17 + $331.40 = $1,044.57